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Schreder L, Luber S. Propagated (fragment) Pipek-Mezey Wannier functions in real-time time-dependent density functional theory. J Chem Phys 2024; 160:214117. [PMID: 38832736 DOI: 10.1063/5.0203442] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2024] [Accepted: 05/14/2024] [Indexed: 06/05/2024] Open
Abstract
Localization procedures are an important tool for analysis of complex systems in quantum chemistry, since canonical molecular orbitals are delocalized and can, therefore, be difficult to align with chemical intuition and obscure information at the local level of the system. This especially applies to calculations obeying periodic boundary conditions. The most commonly used approach to localization is Foster-Boys Wannier functions, which use a unitary transformation to jointly minimize the second moment of the orbitals. This procedure has proven to be robust and fast but has a side effect of often mixing σ- and π-type orbitals. σ/π-separation is achieved by the Pipek-Mezey Wannier function (PMWF) approach [Lehtola and Jónsson, J. Chem. Theory Comput. 10, 642 (2014) and Jónsson et al., J. Chem. Theory Comput. 13, 460 (2017)], which defines the spread functional in terms of partial charges instead. We have implemented a PMWF algorithm in the CP2K software package using the Cardoso-Souloumiac algorithm to enable their application to real-time time-dependent density functional theory. The method is demonstrated on stacked CO2 molecules, linear acetylenic carbon, boron and nitrogen co-doped graphene, and nitrogen-vacancy doped diamond. Finally, we discuss its computational scaling and recent efforts to improve it with fragment approaches.
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Affiliation(s)
- Lukas Schreder
- University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Sandra Luber
- University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
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2
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Schreder L, Luber S. Chiral Spectroscopy of Bulk Systems with Propagated Localized Orbitals. J Chem Theory Comput 2024; 20:3894-3910. [PMID: 38661175 DOI: 10.1021/acs.jctc.4c00235] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/26/2024]
Abstract
We present approaches for the simulation of electronic circular dichroism, Raman, and Raman optical activity (ROA) spectra for isolated and periodic systems as well as subsystem analysis thereof. The method is based on the use of time-dependent maximally localized Wannier functions in the CP2K package and accounts for origin dependencies inherent to the Gaussian and plane wave with pseudopotentials approach as well as the origin dependence of the magnetic dipole and electric quadrupole operators. Tests on the H-bonded enantiomers of alanine by harmonic normal-mode analysis and on an aqueous solution of l-alanine by ab initio molecular dynamics obeying periodic boundary conditions (PBCs) are presented as total and subsystem-resolved spectra. To our knowledge, this is the first instance of an ROA spectrum derived from real-time propagation obeying PBCs and the first ROA simulation considering off-, pre-, and on-resonance effects within PBCs.
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Affiliation(s)
- Lukas Schreder
- University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Sandra Luber
- University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
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Richter R, Aschebrock T, Schelter I, Kümmel S. Meta-generalized gradient approximations in time dependent generalized Kohn-Sham theory: Importance of the current density correction. J Chem Phys 2023; 159:124117. [PMID: 38127400 DOI: 10.1063/5.0167972] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2023] [Accepted: 09/07/2023] [Indexed: 12/23/2023] Open
Abstract
We revisit the use of Meta-Generalized Gradient Approximations (mGGAs) in time-dependent density functional theory, reviewing conceptual questions and solving the generalized Kohn-Sham equations by real-time propagation. After discussing the technical aspects of using mGGAs in combination with pseudopotentials and comparing real-space and basis set results, we focus on investigating the importance of the current-density based gauge invariance correction. For the two modern mGGAs that we investigate in this work, TASK and r2SCAN, we observe that for some systems, the current density correction leads to negligible changes, but for others, it changes excitation energies by up to 40% and more than 0.8 eV. In the cases that we study, the agreement with the reference data is improved by the current density correction.
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Affiliation(s)
- Rian Richter
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
| | - Thilo Aschebrock
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
| | - Ingo Schelter
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
| | - Stephan Kümmel
- Theoretical Physics IV, University of Bayreuth, 95440 Bayreuth, Germany
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Ranka K, Isborn CM. Size-dependent errors in real-time electron density propagation. J Chem Phys 2023; 158:2887545. [PMID: 37125706 DOI: 10.1063/5.0142515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2023] [Accepted: 04/14/2023] [Indexed: 05/02/2023] Open
Abstract
Real-time (RT) electron density propagation with time-dependent density functional theory (TDDFT) or Hartree-Fock (TDHF) is one of the most popular methods to model the charge transfer in molecules and materials. However, both RT-TDHF and RT-TDDFT within the adiabatic approximation are known to produce inaccurate evolution of the electron density away from the ground state in model systems, leading to large errors in charge transfer and erroneous shifting of peaks in absorption spectra. Given the poor performance of these methods with small model systems and the widespread use of the methods with larger molecular and material systems, here we bridge the gap in our understanding of these methods and examine the size-dependence of errors in RT density propagation. We analyze the performance of RT density propagation for systems of increasing size during the application of a continuous resonant field to induce Rabi-like oscillations, during charge-transfer dynamics, and for peak shifting in simulated absorption spectra. We find that the errors in the electron dynamics are indeed size dependent for these phenomena, with the largest system producing the results most aligned with those expected from linear response theory. The results suggest that although the RT-TDHF and RT-TDDFT methods may produce severe errors for model systems, the errors in charge transfer and resonantly driven electron dynamics may be much less significant for more realistic, large-scale molecules and materials.
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Affiliation(s)
- Karnamohit Ranka
- Chemistry and Biochemistry, University of California Merced, Merced, California 95343, USA
| | - Christine M Isborn
- Chemistry and Biochemistry, University of California Merced, Merced, California 95343, USA
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Moitra T, Konecny L, Kadek M, Rubio A, Repisky M. Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy. J Phys Chem Lett 2023; 14:1714-1724. [PMID: 36757216 PMCID: PMC9940299 DOI: 10.1021/acs.jpclett.2c03599] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
First principles theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, especially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time, time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regimes. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near-L2,3-edge TAS processes of experimentally relevant systems and provide additional physical insights using relativistic nonequilibrium response theory.
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Affiliation(s)
- Torsha Moitra
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
| | - Lukas Konecny
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Max
Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Marius Kadek
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Department
of Physics, Northeastern University, Boston, Massachusetts 02115, United States
- Algorithmiq
Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
| | - Angel Rubio
- Max
Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics (CCQ), The Flatiron Institute, 162 Fifth Avenue, New York New York 10010, United States
- Nano-Bio
Spectroscopy Group, Departamento de Física de Materiales, Universidad del País Vasco, 20018 San Sebastian, Spain
| | - Michal Repisky
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Department
of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, 84104 Bratislava, Slovakia
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Trepl T, Schelter I, Kümmel S. Analyzing Excitation-Energy Transfer Based on the Time-Dependent Density Functional Theory in Real Time. J Chem Theory Comput 2022; 18:6577-6587. [PMID: 36268773 DOI: 10.1021/acs.jctc.2c00600] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Excitation-energy transfer is a key step in processes such as photosynthesis that convert light into other forms of energy. Time-dependent density functional theory (DFT) in real time is ideal for the first-principles simulation of such processes due to its computational efficiency. We here demonstrate how real-time DFT can be used for analyzing excitation-energy transfer from first-principles. We discuss several measures of energy transfer that are based solely on the time-dependent density, are well founded in the DFT framework, allow for intuitive understanding and visualization, and reproduce important limiting cases of an analytical model. We demonstrate their usefulness in calculations for model systems, both with static nuclei and in the context of DFT-based Ehrenfest dynamics.
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Affiliation(s)
- T Trepl
- Theoretical Physics IV, University of Bayreuth, Bayreuth95440, Germany
| | - I Schelter
- Theoretical Physics IV, University of Bayreuth, Bayreuth95440, Germany
| | - S Kümmel
- Theoretical Physics IV, University of Bayreuth, Bayreuth95440, Germany
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Mattiat J, Luber S. Comparison of Length, Velocity, and Symmetric Gauges for the Calculation of Absorption and Electric Circular Dichroism Spectra with Real-Time Time-Dependent Density Functional Theory. J Chem Theory Comput 2022; 18:5513-5526. [PMID: 36041170 DOI: 10.1021/acs.jctc.2c00644] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A velocity and symmetric gauge implementation for real-time time-dependent density functional theory (RT-TDDFT) in the CP2K package using a Gaussian and plane wave approach is presented, including the explicit gauge-transformed contributions due to the nonlocal part of pseudopotentials. Absorption spectra of gas-phase α-pinene are calculated in length and velocity gauges in the long-wavelength approximation for the application of a δ pulse in linear and full order. The velocity gauge implementation is also applied to a solvated uracil molecule to showcase its use within periodic boundary conditions (PBC). For the calculation of the expectation value of the electric dipole moment in PBC, both the velocity representation and the modern theory of polarization give equivalent absorption spectra if a distributed reference point is used for the nonlocal term of the velocity operator. The discussion of linear response theory takes place in a unified framework in terms of linear response functions in propagator notation, distinguishing the parts of the linear response functions associated with perturbation and response. To further investigate gauge dependence, electric circular dichroism (ECD) spectra of α-pinene were calculated either as magnetic response to an electric field perturbation, in length or velocity gauge, or as electric response to a magnetic field perturbation in the symmetric gauge. Both approaches, electric and magnetic perturbations, have been found to yield equivalent ECD spectra.
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Affiliation(s)
- Johann Mattiat
- Department of Chemistry, University of Zurich, Zurich 8057, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zurich, Zurich 8057, Switzerland
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